System and method for iq mismatch calibration and compensation

ABSTRACT

A method for providing IQ mismatch (IQMM) compensation includes: sending a single tone signal at an original frequency; determining a first response of an impaired signal at the original frequency and a second response of the impaired signal at a corresponding image frequency; determining an estimate of a frequency response of the compensation filter at the original frequency based on the first response and the second response; repeating the steps of sending the single tone signal, determining the first response and the second response, and determining the estimate of the frequency response of the compensation filter by sweeping the single tone signal at a plurality of steps to determine a snapshot of the frequency response of the compensation filter; converting the frequency response of the compensation filter to a plurality of time-domain filter taps of the compensation filter by performing a pseudo-inverse of a time-to-frequency conversion matrix; and determining a time delay that provides a minimal LSE for the corresponding time domain filter taps.

CROSS-REFERENCE TO RELATED APPLICATION(S)

This application is a divisional application of U.S. patent applicationSer. No. 15/599,294 filed May 18, 2017, which claims the benefits of andpriority to U.S. Provisional Patent Application Ser. No. 62/461,994filed Feb. 22, 2017, the disclosure of which is incorporated herein byreference in its entirety.

TECHNICAL FIELD

The present disclosure relates generally to wireless communicationsystems, more particularly, to a system and method for a system andmethod for IQ mismatch calibration and compensation.

BACKGROUND

In an ideal frequency-modulated (FM) wireless communication receiver, ananalog front end (FE) exhibits an identical amplitude and a phaseresponse on in-phase (I) and quadrature (Q) branches. In practice,however, mismatches and imbalances between the I and Q branches areunavoidable due to operating conditions and imperfections caused by thecomponents of the wireless communication receiver such as a mixer, ananalog low pass filer, and an analog-to-digital converter (ADC). Themismatches and imbalances introduce an image signal at a mirrorfrequency of a baseband frequency that can interfere with a demodulationand/or modulation process of an original signal. The image signal candegrade the performance of the wireless communication receiver. Tomitigate the IQ mismatches and imbalances, numerous IQ mismatchcompensation (IQMC) techniques based on a digital signal processing(DSP) have been proposed.

The IQ mismatches and imbalances are dominant causes of radio frequency(RF) impairments in modern direct-conversion RF receivers. In a typicalIQMC architecture, an adaptive filter can find filter coefficients byiteratively exploring a desired property based on an actual receivedsignal. However, those filter coefficients that are obtained by theiterative process may not meet an increasingly demanding requirement forhigh data rates in emerging wireless communication applications.

SUMMARY

According to one embodiment, a method for providing IQ mismatch (IQMM)compensation includes: sending a single tone signal at an originalfrequency; determining a first response of an impaired signal at theoriginal frequency and a second response of the impaired signal at acorresponding image frequency; determining an estimate of a frequencyresponse of a compensation filter at the original frequency based on thefirst response and the second response; repeating the steps of sendingthe single tone signal, determining the first response and the secondresponse, and determining the estimate of the frequency response of thecompensation filter by sweeping the single tone signal at a plurality ofsteps to determine a snapshot of the frequency response of thecompensation filter; converting the frequency response of thecompensation filter to a plurality of time-domain filter taps of thecompensation filter by performing a pseudo-inverse of atime-to-frequency conversion matrix; and determining a time delay thatprovides a minimal least square error (LSE) based on a plurality of LSEsfor the corresponding time domain filter taps.

According to one embodiment, a method for providing IQ mismatch (IQMM)compensation includes: estimating filter coefficients corresponding to aplurality of filter taps of a compensation filter before reception ofnormal signals based on a static calibration scheme; setting each of theplurality of filter taps with a corresponding estimated filtercoefficient; setting an initial value for a time delay tap to zero orbased an estimated value obtained using the static calibration scheme;and estimating a filter coefficient for the time delay tap duringreception of a normal signal based on an iterative scheme using anadaptive filter.

According to one embodiment, an apparatus includes: a signal generatorfor generating and sending a single tone signal at an originalfrequency; a compensator including a time delay and a plurality oftime-domain filter taps; and a compensation logic for performing astatic calibration of the compensator. The compensation logic isconfigured to: determine a first response of an impaired signal at theoriginal frequency and a second response of the impaired signal at acorresponding image frequency; determine an estimate of a frequencyresponse of a compensation filter at the original frequency based on thefirst response and the second response; repeat the steps of sending thesingle tone signal, determining the first response and the secondresponse, and determining the estimate of the frequency response bysweeping the single tone signal at a plurality of steps to determine asnapshot of the frequency response of the compensation filter; convertthe frequency response of the compensation filter to a plurality oftime-domain filter taps of the compensation filter by performing apseudo-inverse of a time-to-frequency conversion matrix; and determininga time delay that provides a minimal least square error (LSE) based on aplurality of LSEs for the corresponding time domain filter taps.

The above and other preferred features, including various novel detailsof implementation and combination of events, will now be moreparticularly described with reference to the accompanying figures andpointed out in the claims. It will be understood that the particularsystems and methods described herein are shown by way of illustrationonly and not as limitations. As will be understood by those skilled inthe art, the principles and features described herein may be employed invarious and numerous embodiments without departing from the scope of thepresent disclosure.

BRIEF DESCRIPTION OF THE DRAWINGS

The accompanying drawings, which are included as part of the presentspecification, illustrate the presently preferred embodiment andtogether with the general description given above and the detaileddescription of the preferred embodiment given below serve to explain andteach the principles described herein.

FIG. 1 illustrates an exemplary block diagram of an example IQMC system,according to one embodiment;

FIG. 2 illustrates an exemplary diagram of an IQ mismatch model (IQMM),according to one embodiment;

FIG. 3 illustrates an exemplary plot of a non-causal filter coefficientsof a non-causal filter, according to one embodiment;

FIG. 4 illustrates exemplary plots of filter coefficients of a causalfilter, according to one embodiment;

FIG. 5 shows a flowchart of a training-based calibration scheme,according to one embodiment;

FIG. 6 shows an example real-valued filter, according to one embodiment;

FIG. 7 shows a block diagram of an example complex-valued IQMC system,according to one embodiment; and

FIG. 8 shows a block diagram of an example IQMC system, according to oneembodiment.

The figures are not necessarily drawn to scale and elements of similarstructures or functions are generally represented by like referencenumerals for illustrative purposes throughout the figures. The figuresare only intended to facilitate the description of the variousembodiments described herein. The figures do not describe every aspectof the teachings disclosed herein and do not limit the scope of theclaims.

DETAILED DESCRIPTION

Each of the features and teachings disclosed herein can be utilizedseparately or in conjunction with other features and teachings toprovide an IQ mismatch calibration and compensation. Representativeexamples utilizing many of these additional features and teachings, bothseparately and in combination, are described in further detail withreference to the attached figures. This detailed description is merelyintended to teach a person of skill in the art further details forpracticing aspects of the present teachings and is not intended to limitthe scope of the claims. Therefore, combinations of features disclosedabove in the detailed description may not be necessary to practice theteachings in the broadest sense, and are instead taught merely todescribe particularly representative examples of the present teachings.

In the description below, for purposes of explanation only, specificnomenclature is set forth to provide a thorough understanding of thepresent disclosure. However, it will be apparent to one skilled in theart that these specific details are not required to practice theteachings of the present disclosure.

Some portions of the detailed descriptions herein are presented in termsof algorithms and symbolic representations of operations on data bitswithin a computer memory. These algorithmic descriptions andrepresentations are used by those skilled in the data processing arts toeffectively convey the substance of their work to others skilled in theart. An algorithm is here, and generally, conceived to be aself-consistent sequence of steps leading to a desired result. The stepsare those requiring physical manipulations of physical quantities.Usually, though not necessarily, these quantities take the form ofelectrical or magnetic signals capable of being stored, transferred,combined, compared, and otherwise manipulated. It has proven convenientat times, principally for reasons of common usage, to refer to thesesignals as bits, values, elements, symbols, characters, terms, numbers,or the like.

It should be borne in mind, however, that all of these and similar termsare to be associated with the appropriate physical quantities and aremerely convenient labels applied to these quantities. Unlessspecifically stated otherwise as apparent from the below discussion, itis appreciated that throughout the description, discussions utilizingterms such as “processing,” “computing,” “calculating,” “determining,”“displaying,” or the like, refer to the action and processes of acomputer system, or similar electronic computing device, thatmanipulates and transforms data represented as physical (electronic)quantities within the computer system's registers and memories intoother data similarly represented as physical quantities within thecomputer system memories or registers or other such information storage,transmission or display devices.

The algorithms presented herein are not inherently related to anyparticular computer or other apparatus. Various general-purpose systems,computer servers, or personal computers may be used with programs inaccordance with the teachings herein, or it may prove convenient toconstruct a more specialized apparatus to perform the required methodsteps. The required structure for a variety of these systems will appearfrom the description below. It will be appreciated that a variety ofprogramming languages may be used to implement the teachings of thedisclosure as described herein.

Moreover, the various features of the representative examples and thedependent claims may be combined in ways that are not specifically andexplicitly enumerated in order to provide additional useful embodimentsof the present teachings. It is also expressly noted that all valueranges or indications of groups of entities disclose every possibleintermediate value or intermediate entity for the purpose of an originaldisclosure, as well as for the purpose of restricting the claimedsubject matter. It is also expressly noted that the dimensions and theshapes of the components shown in the figures are designed to help tounderstand how the present teachings are practiced, but not intended tolimit the dimensions and the shapes shown in the examples.

The present disclosure provides an IQ mismatch compensation (IQMC)system and method that can mitigate an impact of an IQ mismatch and/oran IQ imbalance using digital signal processing (DSP) techniques. FIG. 1illustrates an exemplary block diagram of an example IQMC system,according to one embodiment. The IQMC system 100 can be implemented asan independent signal receiver or a signal receiver integrated in awireless communication transceiver.

In a time domain, the present IQMC system 100 receives an input signalz(t) (herein also referred to as a mismatched signal or an impairedsignal) that includes mismatches and imbalances and generates a signaly(t) that can compensate the input signal z(t). The input signal z(t) isa complex impaired signal including a real part z_(i)(t) and animaginary part z_(q)(t). The present IQMC system 100 includes a filter113, an operational block 112 that operates on the input signal z(t), adelay block 111 applied to the input signal z(t) on a main path, and anadder block 116 that adds the signals output from the delay block 111and the filter 113.

According to one embodiment, the operational block 112 is a complexconjugate unit that takes a complex conjugate of the input signal z(t).In another embodiment, the operational block 112 is a real unit thattakes a real part of the input signal z(t). In some embodiments, thecomplexity of the conjugate operation performed by the operational block112 can be reduced by taking just the real part of the input signalz(t). The output of the operational block 112 is fed to the filter 113as an input.

According to one embodiment, the IQMC system 100 can include acomplex-valued compensator (CVC) that uses a complex-valued compensationfilter. For example, the input signal z(t) can be a complex-valuedsignal including a real part z_(i)(t) and an imaginary part z_(q)(t),and the filter 113 can be a complex-valued compensation filter.

The output signal from the filter 113 is fed to the adder block 116 thatcombines the filtered signal with the delayed input signal (i.e.,z(t−D)) to generate the compensated signal y(t). Regardless of whetherthe complex conjugate of the input signal z(t) or the real part of theinput signal z(t) is used, the present IQMC system 100 uses a CVCbecause the filter 113 is a complex-valued filter.

According to one embodiment, the present IQMC system 100 can beparameterized by a number of the delay D (for example, delay 2 indicatesa delay of two samples) and a number of filter taps N (N being a numberof filter coefficients) in the filter 113. In general, an optimal delaymay grow as the number of filter taps N in the filter 113 increases. Thepresent IQMC system 100 determines filter coefficients given the numberof filter taps N in the filter 113 and an optimal delay of the delayblock 111.

According to one embodiment, the present IQMC system 100 can provide anIQ mismatch calibration to determine the optimal delay D and the optimalfilter coefficients of the filter 113. In one embodiment, the presentIQMC system 100 employs a sequence of single tone training signals witha baseband frequency to determine the optimal filter coefficients for agiven delay D. The baseband frequency refers to the original frequencyof the received signal. The original signal can occupy a frequency bandof a certain size, for example, 20 MHz. The sequence of signal tonetraining signals can be located within the frequency range samplingdiscrete frequencies within the frequency range, for example, 1 MHzgranularity. The filter coefficients can be estimated by sweeping thesingle tone training signals. In a time domain, the compensated signaly(t) can be expressed as a function of the input signal z(t) with adelay D and a filter coefficient w(t):

y(t)=z(t−D)+w(t)*real{z(t)}.  (Eq. 1)

In Eq. 1, a real unit is used as the operational block 112 as anexample, a complex conjugate unit can be used without deviating from thescope of the present disclosure.

FIG. 2 illustrates an exemplary diagram of an IQ mismatch model (IQMM),according to one embodiment. The IQMM shown in FIG. 2 is based on I/Qdown-conversion. The output of the IQMM is fed to the IQMC system 100 ofFIG. 1. The IQMM 200 can demodulate and split a received signal s(t)into in-phase (I) and quadrature (Q) signals paths. Each of the I and Qpaths includes a mixer (211 and 212 respectively) and an analog filter(h₁(t) and h₂(t)). The mixers 211 and 212 output down-converted signalsm_(i)(t) and m_(q)(t) on the I and Q paths, respectively using a localoscillator (LO) whose frequency is ω_(LO). The down-converted signalsm_(i)(t) and m_(q)(t) are filtered by the analog filters h₁(t) and h₂(t)to generate the output signals z_(i)(t) and z_(q)(t) respectively on theI and Q paths. The signals on the I and Q paths can introduce mismatchesand imbalances including: 1) mismatches of a gain g and a phase ϕ at themixers 211 and 212 and 2) overall frequency responses of the analogfilters h₁(t) and h₂(t).

The present IQMM can be either a frequency independent (FI)-IQMM or afrequency dependent (FD)-IQMM. The IQMM shown in FIG. 2 can be eitherthe FI-IQMM or the FD-IQMM. The FI-IQMM can be applied to a signalhaving a non-unity gain g≠1 and a non-zero phase ϕ≠0. The FD-IQMM caninclude analog filters h₁(t) and h₂(t), where h₁(t) is an impulseresponse of an analog filter along the I path, and h₂(t) is an impulseresponse of an analog filter along the Q path.

The received signal s(t) that is demodulated and split into I and Qpaths can include a desired original signal, and an image signalrepresenting a gain and/or phase imbalance introduced onto the desiredoriginal signal a result of signal processing by the mixers 211 and 212and the analog filters h₁(t) and h₂(t) of the IQMM 200. The present IQMCsystem attempts to minimize the impact of the image signal.

The mismatched signal z(t) of the IQMM 200 can be expressed as afunction of the received signal s(t) and an image signal s*(t). Forexample, the mismatched signal z(t) can be expressed as:

z(t)=g ₁(t)*s(t)+g ₂(t)*s*(t),  (Eq. 2)

where

g ₁(t)=(h ₁(t)+ge ^(−jØ) h ₂(t))/2

g ₂(t)=(h ₁(t)−ge ^(jØ) h ₂(t))/2  (Eq. 3).

g₁(t) and g₂(t) denote complex scaling factors for the received signals(t) and the image signal s*(t). For example, the scaling factor g₁(t)is an impulse response of the effective filter that the original signalpasses through, and the scaling factor g₂ (t) is an impulse response ofthe effective filter that the image signal that is introduced by the IQmismatch passes through. The mismatched signal z(t) of Eq. 2 can berepresented in an equation of a frequency domain using a Fouriertransform:

Z(f)=G ₁(f)S(f)+G ₂(f)S*(f),  (Eq. 4)

where

$\begin{matrix}{{{G_{1}(f)} = \frac{{H_{1}(f)} + {{ge}^{{- j}\; \varnothing}{H_{2}(f)}}}{2}}{{G_{2}(f)} = {\frac{\left( {{H_{1}(f)} - {{ge}^{j\; \varnothing}{H_{2}(f)}}} \right)}{2}.}}} & \left( {{Eq}.\mspace{14mu} 5} \right)\end{matrix}$

Referring to the present IQMC system shown in FIG. 1, the compensatedsignal y(t) can be expressed in terms of the complex scaling factorsg₁(t) and g₂(t), the received signal s(t) and the image signal s*(t) as:

$\begin{matrix}\begin{matrix}{{y(t)} = {{z\left( {t - D} \right)} + {{w(t)}*{real}\left\{ {z(t)} \right\}}}} \\{= {{\left( {{g_{1}\left( {t - D} \right)} + {\frac{1}{2}{w(t)}*\left( {{g_{2}^{*}(t)} + {g_{1}(t)}} \right)}} \right)*{s(t)}} +}} \\{{\left( {{g_{2}\left( {t - D} \right)} + {\frac{1}{2}{w(t)}*\left( {{g_{1}^{*}(t)} + {g_{2}(t)}} \right)}} \right)*{{s^{*}(t)}.}}}\end{matrix} & \left( {{Eq}.\mspace{14mu} 6} \right)\end{matrix}$

From Eq. 6, the optimal filter coefficient w(t) that can completelycancel the image signal s*(t) can be obtained by forcingg₂(t−D)+½w(t)*(g₁*(t)+g₂(t))=0. This leads to an optimal filtercoefficient W_(OPT) (f) in a frequency domain:

$\begin{matrix}\begin{matrix}{{W_{OPT}(f)} = {{- \frac{2G_{2}(f)}{{G_{1}^{*}\left( {- f} \right)} + {G_{2}(f)}}}e^{{- j}\; 2\pi \; f\; D}}} \\{= {\left( {{- 1} + {{ge}^{j\mspace{11mu} \varnothing}\frac{H_{2}(f)}{H_{1}(f)}}} \right){e^{{- j}\; 2\pi \; {fD}}.}}}\end{matrix} & \left( {{Eq}.\mspace{14mu} 7} \right)\end{matrix}$

In the example of the IQMM shown in FIG. 2, the optimal filter is anon-causal filter with a large number of filter taps. A causal filterhas zero values at negative indices of filter taps. In contrast, anon-causal filer can have non-zero values at negative indices of filtertaps. FIG. 3 illustrates an exemplary plot of filter coefficients of anon-causal filter, according to one embodiment.

According to one embodiment, the present IQMM is based on a polemismatch between two third-order Butterworth filters on the I and Qpaths. The example in FIG. 3 shows filter taps that span from −20 to 20of a complex-valued optimal filter showing only the real part. Theoptimal filter corresponds to an IQMM model with a 40 MHz third-orderButterworth filter with a pole mismatch [2%, 2%, 2%], a gain mismatch0%, and a phase mismatch of 0 degree. The negative filter taps havenon-zero values; therefore, the filter is a non-causal filter.

According to one embodiment, the optimal filter is approximated with acausal filter with a finite number of filter taps. Herein, the optimalfilter may refer to a causal optimal filter with a finite number offilter taps that is an approximate of the non-causal optimal filter witha large number of filter taps. When approximating the optimal filterW_(OPT) with a finite number of filter taps, one or more negative tapscan be included. FIG. 4 illustrates exemplary plots of filtercoefficients of a causal filter, according to one embodiment.

In the case of a causal filter, the optimal filter can be approximatedwith a finite impulse response (FIR) filter by truncating the optimalfilter by selecting only a finite number of filter taps N. The FIRfilter has a finite number of taps. The FIR filter can be a non-causalfilter if there is at least one negative tap. In the example shown inFIG. 4, the FIR filter without a delay includes the filter taps 0 to 4that have large energy/magnitude excluding the negative taps. However,it is observed that the filter tap −1 of the optimal filter has amagnitude that is larger than a magnitude of the filter tap 4. In thiscase, one can include the filter tap −1. In order to select the filtertap −1, an extra delay can be introduced on a feedthrough path (e.g., inthe delay block 111) such that the filter taps −1 through 3 are alleffectively shifted right by 1 unit to occupy the filter tap 0 through4. The unit herein refers to the number of sample, and its value is thesame value as the value of the delay D samples introduced in the delayblock 111 of FIG. 1. Thus, the extra delay can improve the filteringperformance of the optimal filter. In this case, impairment parametersof the IQMM are assumed to be known so that the FIR approximation of theoptimal filter can be determined based on the IQMM impairmentparameters. In practice, however, the impairment parameters of the IQMMmay not be available a priori, and a training scheme may be used toobtain the impairment parameters.

According to one embodiment, the present IQMC system can estimate filtercoefficients of the compensator filter using one or more pilot singletone signals. For example, the present IQMC system providestraining-based IQMC calibration using one or more pilot single tonesignals. The training-based IQMC calibration starts with sending asingle tone signal at a selected frequency within the frequency range ofthe desired signal. The present IQMC system observes and analyzesresponses of the impaired signal (i.e., received signal withoutcompensation) at both an original frequency of a received signal and theimage frequency. Based on the responses at both the original frequencyand the image frequency, the present IQMC system can estimate a responseof the compensator filter at other frequencies as well. The present IQMCsystem can sweeps the single tone over a range of frequencies at certainsteps to obtain a snapshot of the frequency response of the compensatorfilter over the range of frequencies. The present IQMC system convertsthe frequency response of the compensator filter to time domain taps byperforming a pseudo-inverse of a time-to-frequency conversion matrix.The present IQMC system can check the frequency responses of thecompensation filter by applying different delays with the same set ofsingle tone signals.

According to one embodiment, the present IQMC system generates Kcontinuous-time single tone signals at a selected frequency f_(p) _(k) .The selected frequency f_(p) _(k) can be a multiple of subcarriersspacing, according to one embodiment. For each k∈{1, . . . , K}, usingdiscrete time Fourier transform (DTFT), the present IQMC system uses adiscrete time Fourier transform (DTFT) to determine a frequencycomponent of the received time domain signal z(t) at normalizedfrequencies f_(p) _(k) /f_(s) and −f_(p) _(k) /f_(s) that are denoted asZ(f_(p) _(k) /f_(s)) and Z(−f_(p) _(k) /f_(s)). The sampling frequencyat a point where the received signal is processed is denoted as f_(s):

$\begin{matrix}{{Z\left( \frac{f}{f_{s}} \right)} = {\sum\limits_{m = 0}^{M - 1}{{z(m)}{e^{{- j}\; 2\pi \; \frac{f}{f_{s}}m}.}}}} & \left( {{Eq}.\mspace{14mu} 8} \right)\end{matrix}$

The following quantity is determined by:

$\begin{matrix}{{- \frac{2{Z\left( {- \frac{f_{p_{k}}}{f_{s}}} \right)}}{{Z^{*}\left( \frac{f_{p_{k}}}{f_{s}} \right)} + {Z\left( {- \frac{f_{p_{k}}}{f_{s}}} \right)}}} = {{W^{\prime}\left( {- f_{p_{k}}} \right)}.}} & \left( {{Eq}.\mspace{14mu} 9} \right)\end{matrix}$

For each D∈{0, . . . , N−1}, the present IQMC system determines:

$\begin{matrix}{{W_{D}\left( {- f_{p_{k}}} \right)} = {{W^{\prime}\left( {- f_{p_{k}}} \right)}{e^{{- j}\; 2\pi \; {D{({- \frac{f_{p_{k}}}{f_{s}\;}})}}}.}}} & \left( {{Eq}.\mspace{14mu} 10} \right)\end{matrix}$

By denoting

W^(′) = [W^(′)(−f_(p₁)), …  , W^(′)(−f_(p_(k)))]^(T), W_(D) = [W_(D)(−f_(p₁)), …  , W_(D)(−f_(p_(k)))]^(T), and${D = {{diag}\left( {e^{{- j}\; 2\pi \; {D{({- \frac{f_{1}}{f_{s}}})}}},\ldots \mspace{14mu},e^{{- j}\; 2\pi \; {D{({- \frac{f_{K}}{f_{s}}})}}}} \right)}},$

this step can be also written in the following matrix form:

W _(D) =DW′.  (Eq. 11)

A K×N discrete time Fourier (DFT) matrix is denoted as F, whose entriesare given by:

F_(k, n) = e^(−j 2π(−f_(p_(k))/f_(s_(iqmc)))n),where k∈{1, . . . ,K} and n∈{0, . . . ,N−1},  (Eq. 12).

f_(s) _(iqmc) is an operating frequency at which the present IQMCoperates.

According to one embodiment, the present IQMC system precomputes andstores a pseudo inverse of the DFT matrix F as:

pinv(F)=(F ^(H) F)⁻¹ F ^(H).  (Eq. 13)

The present IQMC system loads the pseudo inverse of the DFT matrix F andcomputes the N-tap FIR approximation w_(opt,N,D) of the optimal filteras:

w _(opt,N,D) =pinv(F)W _(D) =pinv(F)DW′.  (Eq. 14)

In another embodiment, the present IQMC system precomputes pinv(F)D forevery delay D and loads the product altogether to avoid computing amatrix product of three matrices pinv(F), D, and W′. For eachw_(opt,N,D,) the present IQMC system can compute a least square errorthat is defined as:

LSE_(D) =∥W _(D) −Fw _(opt,N,D)∥².  (Eq. 15)

The present IQMC system selects an optimal delay D that yields theminimal least square error (LSE) using the following equation:

$\begin{matrix}{D = {\arg \; {\min\limits_{D}{{LSE}_{D}.}}}} & \left( {{Eq}.\mspace{14mu} 16} \right)\end{matrix}$

In this case, the least square error between the desired frequencyresponse and the frequency response of the designed filter is a metricused to select the optimal delay D.

In an ideal condition, a static calibration scheme can find all filtercoefficients for a given tuple of parameters including a signalbandwidth, a frequency band, and a frequency channel. However, inpractice, the number of possible combinations of these three parametersare so large, and the number of static calibrations for each combinationis greatly limited. In order to reduce the complexity, a staticcalibration scheme may be performed for each possible signal bandwidthwith one arbitrarily chosen pair of frequency band and frequencychannel. It is noted that the present static calibration scheme cancompensate for both FI-IQMM and FD-IQMM for a given a band, channel,signal bandwidth configuration. FI-IQMM is varying across band/channel,so FI-IQMM may not be practical to apply the present static calibrationscheme for all possibilities of the three parameters. A hybridcalibration scheme will be described with respect to the followingexamples.

According to one embodiment, the present IQMC system can perform astatic calibration for each bandwidth to determine all but one filtercoefficient. The one filter coefficient corresponds to the value of thetap D, and the tap D is the delay value used in delay block 111 inFIG. 1. In this embodiment, the present IQMC system determines thefilter coefficient for tap D that may change across band/channel basedon an adaptive process. The adaptive process uses the normal receivedsignal instead of a single tone training signal. The adaptive processfinds the value of the tap D given a chose number of filter taps and adelay value D. The present IQMC system can determine the improvements ofthe original filter coefficients that are obtained by the staticcalibration scheme based on a convergence of the remaining filtercoefficients. It is known that the convergence is guaranteed forcommercial wireless standards such as LTE, 3G, and Wi-Fi.

The FD-IQMM is not channel/band dependent because the FD-IQMM is mainlyintroduced by a mismatch between two analog filters that is onlybandwidth dependent but not channel or band dependent. On the otherhand, the FI-IQMM is channel/band dependent because the FI-IQMM ismainly introduced at a mixer that is channel/band dependent. Based onthese observations, the present IQMC system separates the compensationof the FI-IQMM and the FD-IQMM.

According to one embodiment, a ratio of the analog filters

$\frac{H_{2}(f)}{H_{1}(f)}$

is defined as H_(d)(f), and its time-domain impulse response is definedas h_(d)(n). The time-domain response w_(opt)(t) of W_(opt)(f) can beexpressed as:

w _(opt)(n)=−δ(t−D)+ge ^(jØ) h _(d)(n−D).  (Eq. 17)

For the filter tap D, it mainly depends on the FI-IQMM:

w _(opt)(D)=−1+ge ^(jØ) ^(train) h _(d)(0)≈−1+ge ^(jØ).  (Eq. 18)

For other taps, if the filter coefficients can be obtained in a trainingchannel by:

w _(opt) _(train) (n)g _(train) e ^(jØ) ^(train) h _(d)(n−D),n≠D,  (Eq.19)

the time-domain response w_(opt)(t) can depend on both the FI-IQMM andthe FD-IQMM. Herein, the training channel refers to an arbitrarilychosen band and an arbitrarily chosen channel for a specific wirelessstandard (e.g., LTE, 3G, and Wi-Fi). The time-domain response w_(opt)_(train) (n), n≠D may be applied to other test channels. In this case,the actual coefficients for n≠D in the test channel can be given by:

w _(opt) _(test) (n)=g _(test) e ^(jØ) ^(test) h _(d)(n−D),n≠D.  (Eq.20)

As a result, an error in the form of a ratio between the actual valueand the applied value can be expressed by:

$\begin{matrix}{{r_{e} = {\frac{w_{{opt}_{test}}(n)}{w_{{opt}_{train}\;}(n)} = {\frac{g_{test}e^{j\; \varnothing_{test}}{h_{d}\left( {n - D} \right)}}{g_{train}e^{j\; \varnothing_{train}}{h_{d}\left( {n - D} \right)}} = \frac{g_{test}e^{j\; \varnothing_{test}}}{g_{train}e^{j\; \varnothing_{train}}}}}},\mspace{20mu} {n \neq {D.}}} & \left( {{Eq}.\mspace{14mu} 21} \right)\end{matrix}$

If the FI-IQMM does not change too much, the error may not be large, andthe performance may be acceptable. If the error is large, the error maybe compensated as follows:

w _(opt) _(train) (D)+1=g _(train) e ^(jØ) ^(train) h _(d)(0) and

w _(opt) _(test) (D)+1=g _(test) e ^(jØ) ^(test) h _(d)(0).  (Eq. 22)

It is observed that the error r_(e) can be estimated from w_(opt)_(train) (D) and w_(opt) _(test) (D) as:

$\begin{matrix}{= {\frac{{w_{{opt}_{test}}(D)} + 1}{{w_{{opt}_{train}}(D)} + 1} = {\frac{g_{test}e^{j\; \varnothing_{test}}{h_{d}(0)}}{g_{train}e^{j\; \varnothing_{train}}{h_{d}(0)}} = {\frac{g_{test}e^{j\; \varnothing_{test}}}{g_{train}e^{j\; \varnothing_{train}}} = {r_{e}.}}}}} & \left( {{Eq}.\mspace{14mu} 23} \right)\end{matrix}$

From

and w_(opt) _(train) (n), w_(opt) _(test) (n) may be obtained asfollows. According to one embodiment, given selected filter taps N and adelay D, the present IQMC system estimates all filter coefficientsbefore the reception of normal signals using a pilot-based scheme. Inone embodiment, the present IQMC system estimates the filtercoefficients using a static calibration scheme employing a sequence ofsingle tone training signals as described above.

The present IQMC system further sets all filter taps except the filtertap D with the estimated filter coefficient values. An initial value ofthe filter tap D may be set in several ways. In one embodiment, thepresent IQMC system sets the filter tap D value to be 0. In anotherembodiment, the present IQMC system sets the filter tap D value to anestimated value obtained using the pilot-based scheme. The filter tap Dthat is estimated based on the pilot-based scheme can shorten aconvergence time to determine the optimal filter coefficients. Here, thefilter coefficients may be denoted as w_(opt,N) _(train) (0), . . . ,w_(opt,N) _(train) (N−1).

During the reception of a normal signal, the present IQMC systemperforms an adaptive process only for the filter tap D as describedbelow:

Input/output Signal z(n), y(n) Parameters Z(n) = [z(n) z(n − 1) . . .z(n − N + 1)]^(T) Y(n) = [y(n) y(n − 1) . . . y(n − N + 1)]^(T) W(n) =[w₀(0) . . . w_(D)(n) . . . w_(N−1)(0)]^(T) Step Size: μ For n = 0,1, .. . y(n) = z(n − D) + W^(T)(n)real(Z(n)) or y(n) = z(n − D) +W^(T)(n)Z*(n) Update w_(D)(n + 1) = w_(D)(n) − μy(n − i)y(n − i), forany i ϵ {0, . . . , N − 1}

According to one embodiment, after the filter tap D is converged tow_(ada) _(test) (D), the present IQMC system may further determine acorrection factor

as follows:

$\begin{matrix}{= {\frac{{w_{{ada}_{test}}(D)} + 1}{{w_{{opt},N_{train}}(D)} + 1}.}} & \left( {{Eq}.\mspace{11mu} 24} \right)\end{matrix}$

The present IQMC system can then update all other filter taps asfollows:

$\begin{matrix}{{{w_{test}(n)} = {\cdot {w_{{opt},N_{train}}(n)}}},{n \neq {D.}}} & \left( {{Eq}.\mspace{14mu} 25} \right)\end{matrix}$

FIG. 5 shows a flowchart of a training-based calibration scheme,according to one embodiment. According to one embodiment, the presentIQMC system provides a training-based calibration scheme for calibratinga compensator filter. First, the present IQMC system sends a single tonesignal at a selected frequency (at 501). The present IQMC systemdetermines a frequency response of an impaired signal at an originalfrequency and a corresponding image frequency (at 502). The present IQMCsystem determines an estimate of a frequency response of thecompensation filter based on the frequency response at the originalfrequency and the image frequency (at 503). The present IQMC systemrepeats the calibration steps performed in 501-503 by sweeping thesingle tone at a plurality of steps (multiples of subcarriers spacing)to obtain a snapshot of the frequency response of the compensationfilter (at 504). The present IQMC system converts the frequency responseof the compensation filter to determine optimal time-domain filter tapsof the compensation filter (at 505). For example, the present IQMCsystem performs a pseudo-inverse of a time-to-frequency conversionmatrix for the frequency-to-time domain conversion. The present IQMCsystem repeats the static calibration steps performed in 501-505 byapplying different delays with the same set of single tone signals andcheck the frequency responses of the impaired signal (at 506). Thepresent IQMC system then determines an optimal delay that provides aminimal least square error (LSE) for the corresponding time-domainfilter taps (at 507). The present training-based calibration scheme caneffectively compensate mismatches and imbalances of a FD-IQMM, and thesame baseband filtering can be applied across channels for a givenbandwidth. Furthermore, the training-based calibration scheme cancompensate mismatches and imbalances of a FI-IQMM.

The present IQMC system may further compensate FI-IQMM that variesacross channels due to changes in mixer setting. Before the reception ofnormal signals, the present IQMC system estimates filter coefficientsfor a plurality of filter taps N based on the above-described trainingbased calibration scheme. It is appreciated that the present IQMC systemmay use other pilot-based static calibration schemes without deviatingfrom the scope of the present disclosure. The present IQMC system setsall N filter taps with corresponding estimated filter coefficients(these filter coefficients do not change across band/channel), sets aninitial value for delay tap D based on value 0 or an estimated valueobtained using the pilot-based static calibration scheme, and estimatesa filter coefficient (this filter coefficient changes acrossband/channel) for delay tap D during reception of normal signal based onan adaptive filter based iterative scheme. The present IQMC system canfurther improve the estimated filter coefficients for all N filter tapsusing a converged filter coefficient for delay tap D.

According to some embodiments, the present IQMC system uses areal-valued filter. FIG. 6 shows an example real-valued filter,according to one embodiment. The real-valued filter can apply differentfiltering schemes on the Q and I paths. u_(i)(t) and u_(g)(t) are a pairof the impaired signal. The impaired signal is a partially compensatedsignal, and y(t) is the finally compensated signal. The compensationoccurs at two stages. The first stage is used to compensate FD-IQMM, andthe gain mismatch part of FI-IQMM. The second stage is used tocompensate the phase mismatch part of FI-IQMM. The real-valued filterincludes a real-valued scaling factor that feeds a delayed version of anin-phase (I) path into an output of a real-valued filter of a quadrature(Q) path.

The performance of the real-valued filter 600 can match the performanceof the complex-valued filter in a similar setup with appropriateadjustment of the filtering scheme. Moreover, the real-valued filter 600has a simpler structure compared to a complex-valued filter. The simplestructure of the real-valued filter can reduce a gate count of acompensator block.

FIG. 7 shows a block diagram of an example complex-valued IQMC system,according to one embodiment. The functional blocks of the complex-valuedIQMC system 700 include a first complex-valued filter 711 on a mainpath, a second complex-valued filter 713 on a feedthrough path, anoperational block 712 that operates on the input signal Z(f), and anadder block 716 that adds the signals output from the firstcomplex-valued filter 711 and the second complex-valued filter 713. Themapping of the real-valued compensator and the complex-valuedcompensator is based on a mathematical relationship between the impairedsignal and the compensated signal. In an actual implementation, thesetwo compensators can be completely different. FIG. 1 shows thecomplex-valued compensator while FIG. 6 shows the real-valuedcompensator.

The complex-valued IQMC system 700 can be implemented as a signalreceiver in a wireless communication system. The present complex-valuedIQMC system 700 is expressed in terms of a frequency domain. Forexample, the mismatched signal is denoted as Z(f) (herein also referredto as an impaired signal) as an input to generate a compensated signalY(f). The present complex-valued IQMC system 700 is expressed as anequivalent of a complex-valued IQMC system 100 shown in FIG. 1 includingcomplex-valued filters 711 and 713. The operational block 712 is acomplex conjugate unit that takes a complex conjugate of the inputsignal Z(f).

In a time-domain, the discrete compensated signal y[k] at the output ofthe real-valued compensator is expressed as:

$\begin{matrix}\begin{matrix}{{y\lbrack k\rbrack} = {{u_{I}\left\lbrack {k - T_{D}} \right\rbrack} + {j\left( {{\alpha \; {u_{I}\left\lbrack {k - T_{D}} \right\rbrack}} + {{u_{Q}\lbrack k\rbrack}*{\hat{d}\lbrack k\rbrack}}} \right)}}} \\{= {{\frac{1}{2}\left( {{u\left\lbrack {k - T_{D}} \right\rbrack} + {u^{*}\left\lbrack {k - T_{D}} \right)}} \right)} +}} \\{{j\left( {{\frac{\alpha}{2}\left( {{u\left\lbrack {k - T_{D}} \right\rbrack} + {u^{*}\left\lbrack {k - T_{D}} \right\rbrack}} \right)} + {\frac{1}{2j}\left( {{u\lbrack k\rbrack} - {u^{*}\lbrack k\rbrack}} \right)*{\hat{d}\lbrack k\rbrack}}} \right)}} \\{= {{\left( {{\frac{1 + {j\; \alpha}}{2}{\delta \left\lbrack {k - T_{D}} \right\rbrack}} + {\frac{1}{2}{\hat{d}\lbrack k\rbrack}}} \right)*{u(k)}} +}} \\{{\left( {{\frac{1 + {j\; \alpha}}{2}{\delta \left\lbrack {k - T_{D}} \right\rbrack}} - {\frac{1}{2}{d\lbrack k\rbrack}}} \right)*{u^{*}(k)}}} \\{= {{{w_{1}\lbrack k\rbrack}*{u(k)}} + {{w_{2}\lbrack k\rbrack}*{u^{*}(k)}}}}\end{matrix} & \left( {{Eq}.\mspace{14mu} 26} \right)\end{matrix}$

In a frequency domain, the compensated signal is expressed as:

$\begin{matrix}\begin{matrix}{{Y(f)} = {{\left( {{\frac{1 + {j\; \alpha}}{2}e^{{- j}\; 2\pi \; {fT}_{D}}} + {\frac{1}{2}{\hat{D}(f)}}} \right){Z(f)}} +}} \\{{\left( {{\frac{1 + {j\; \alpha}}{2}e^{{- j}\; 2\pi \; {fT}_{D}}} - {\frac{1}{2}{\hat{D}(f)}}} \right){Z^{*}\left( {- f} \right)}}} \\{= {{{W_{1}(f)}{Z(f)}} + {{W_{2}(f)}{Z^{*}\left( {- f} \right)}}}}\end{matrix} & \left( {{Eq}.\mspace{14mu} 27} \right)\end{matrix}$

The Eq. 27 shows a mathematical model for the CVC, and the IRR for theCVC can be calculated. Using the Eq. 27, the RVC can be expressed as anequivalent CVC. After the RVC is written in a form equivalent to a CVC,the IRR of the RVC can be calculated in an analogous manner as discussedabove. The input and the output of the RVC can be written in ananalogous form. W₁(f) and W₁(f) are a function of parameters used in theRVC. The IRR of the RVC can be computed using the Eq. 27 as well.

FIG. 8 shows a block diagram of an example IQMC system, according to oneembodiment. The IQMC system 810 includes a signal generator 811, an IQcompensation logic 812, and an IQ compensator 813. According to oneembodiment, the IQ compensator 813 can implement a delay block and acompensation filter including a plurality of time-domain filter taps asshown in FIG. 1. The IQ compensation logic may be implemented with ahardware digital signal processing chip or in a firmware of a receiverin a wireless communication system.

According to one embodiment, the IQ compensation logic 812 provides astatic calibration of the IQ compensator 813. The signal generator 811is configured to generate a single tone signal. According to oneembodiment, the IQ compensation logic 812 determines a frequency of thesingle tone signal and instructs the signal generator 811 to send thesingle tone signal of the selected frequency. The signal generator 811may send a series of single tone signals to the IQMC system by sweepingthe frequency over a predetermined range of frequencies. The IQcompensation logic 812 receives an impaired signal in response to eachof the series of single tone signals, determines an estimate of afrequency response of the compensation filter, and converts theestimated frequency response of the compensation filter into atime-domain response to determine optimal time-domain filter taps of thecompensation filter. The IQ compensation logic 812 further analyzes anoverall frequency response of the impaired signal over the predeterminedrange of frequencies. Using the overall frequency response of theimpaired signal, the IQ compensation logic 812 determines an optimaltime delay of the delay block and coefficients of the filter taps of thecompensation filter of the IQ compensator 813. For example, the IQcompensation logic 812 generates a time-to-frequency conversion matrixand converts the frequency response of the compensation filter to atime-domain response using a pseudo-inverse of the time-to-frequencyconversion matrix.

According to one embodiment, the IQ compensation logic 812 provides anadaptive calibration of the IQ compensator 813 to optimize the timedelay of the delay block and the filter taps of the compensation filterof the IQ compensator 813. The IQ compensation logic 812 repeats thestatic calibration of the IQ compensator 813 using a plurality of delayvalues with the same set of single tone signals. The IQ compensationlogic 813 determines an optimal delay that provides a minimal leastsquare error (LSE) among the plurality of delay values.

According to one embodiment, a method for providing IQ mismatch (IQMM)compensation includes: sending a single tone signal at an originalfrequency; determining a first response of an impaired signal at theoriginal frequency and a second response of the impaired signal at acorresponding image frequency; determining an estimate of a frequencyresponse of a compensation filter at the original frequency based on thefirst response and the second response; repeating the steps of sendingthe single tone signal, determining the first response and the secondresponse, and determining the estimate of the frequency response of thecompensation filter by sweeping the single tone signal at a plurality ofsteps to determine a snapshot of the frequency response of thecompensation filter; converting the frequency response of thecompensation filter to a plurality of time-domain filter taps of thecompensation filter by performing a pseudo-inverse of atime-to-frequency conversion matrix; and determining a time delay thatprovides a minimal least square error (LSE) based on a plurality of LSEsfor the corresponding time domain filter taps.

The time-to-frequency conversion matrix may be obtained by performing adiscrete time Fourier (DFT) on the snapshot of the frequency response ofthe compensation filter.

The method may further include selecting a finite number of filter tapsamong the plurality of time-domain filter taps.

The finite number of filter taps may include one or more positive filtertaps.

The method may further include adding an extra time delay in afeedforward path of the compensation filter to include a negative filtertap.

The compensation filter may be a complex-valued filter.

The compensation filter may be a real-valued filter including areal-valued scaling factor that feeds a delayed version of an in-phase(I) path into an output of a real-valued filter of a quadrature (Q)path.

The compensation filter may be implemented in a receiver of a wirelesscommunication system.

The compensation filter may include a baseband digital filter.

The method may further include: estimating filter coefficients for theplurality of time-domain filter taps before reception of normal signalsbased on a static calibration scheme; setting each of the plurality oftime-domain filter taps with a corresponding estimated filtercoefficient; setting an initial value for a time delay tap to zero orbased on an estimated value obtained using the static calibrationscheme; and estimating a filter coefficient for the time delay tap usinga normal signal based on an iterative scheme using an adaptive filter.

According to one embodiment, a method for providing IQ mismatch (IQMM)compensation includes: estimating filter coefficients corresponding to aplurality of filter taps of a compensation filter before reception ofnormal signals based on a static calibration scheme; setting each of theplurality of filter taps with a corresponding estimated filtercoefficient; setting an initial value for a time delay tap to zero orbased an estimated value obtained using the static calibration scheme;and estimating a filter coefficient for the time delay tap duringreception of a normal signal based on an iterative scheme using anadaptive filter.

The IQMM may be a frequency-dependent IQMM (FD-IQMM) or afrequency-independent IQMM (FI-IQMM).

The compensation filter may be a complex-valued filter.

The compensation filter may be a real-valued filter including areal-valued scaling factor that feeds a delayed version of an in-phase(I) path into an output of a real-valued filter of a quadrature (Q)path.

The compensation filter may be implemented in a receiver of a wirelesscommunication system.

The compensation filter may include a baseband digital filter.

According to one embodiment, an apparatus includes: a signal generatorfor generating and sending a single tone signal at an originalfrequency; a compensator including a time delay and a plurality oftime-domain filter taps; and a compensation logic for performing astatic calibration of the compensator. The compensation logic isconfigured to: determine a first response of an impaired signal at theoriginal frequency and a second response of the impaired signal at acorresponding image frequency; determine an estimate of a frequencyresponse of a compensation filter at the original frequency based on thefirst response and the second response; repeat the steps of sending thesingle tone signal, determining the first response and the secondresponse, and determining the estimate of the frequency response bysweeping the single tone signal at a plurality of steps to determine asnapshot of the frequency response of the compensation filter; convertthe frequency response of the compensation filter to a plurality oftime-domain filter taps of the compensation filter by performing apseudo-inverse of a time-to-frequency conversion matrix; and determininga time delay that provides a minimal least square error (LSE) based on aplurality of LSEs for the corresponding time domain filter taps.

The compensation logic may further be configured to select a finitenumber of filter taps among the plurality of time-domain filter taps.

The finite number of filter taps may include one or more positive filtertaps.

The compensation logic may further be configured to add an extra timedelay in a feedforward path of the compensation filter to include anegative filter tap.

The compensation filter may be a complex-valued filter.

The compensation filter may be a real-valued filter including areal-valued scaling factor that feeds a delayed version of an in-phase(I) path into an output of a real-valued filter of a quadrature (Q)path.

The compensation logic may further be configured to: estimate filtercoefficients for the plurality of time-domain filter taps beforereception of normal signals based on a static calibration scheme; seteach of the plurality of time-domain filter taps with a correspondingestimated filter coefficient; set an initial value for a time delay tapto zero or based on an estimated value obtained using the staticcalibration scheme; and estimate a filter coefficient for the time delaytap using a normal signal based on an iterative scheme using an adaptivefilter.

The above example embodiments have been described hereinabove toillustrate various embodiments of implementing a system and method forproviding an IQ mismatch calibration and compensation. Variousmodifications and departures from the disclosed example embodiments willoccur to those having ordinary skill in the art. The subject matter thatis intended to be within the scope of the present disclosure is setforth in the following claims.

What is claimed is:
 1. A method for providing IQ mismatch (IQMM)compensation, the method comprising: estimating filter coefficientscorresponding to a plurality of time-domain filter taps of acompensation filter before reception of normal signals based on a staticcalibration scheme; setting each of the plurality of time-domain filtertaps with a corresponding estimated filter coefficient; setting aninitial value for a time delay tap to zero or based an estimated valueobtained using the static calibration scheme; and estimating a filtercoefficient for the time delay tap during reception of a normal signalbased on an iterative scheme using an adaptive filter.
 2. The method ofclaim 1, wherein the IQMM is a frequency-dependent IQMM (FD-IQMM) or afrequency-independent IQMM (FI-IQMM).
 3. The method of claim 1, whereinthe compensation filter is a complex-valued filter.
 4. The method ofclaim 1, wherein the compensation filter is a real-valued filterincluding a real-valued scaling factor that feeds a delayed version ofan in-phase (I) path into an output of a real-valued filter of aquadrature (Q) path.
 5. The method of claim 1, wherein the compensationfilter is implemented in a receiver of a wireless communication system.6. The method of claim 1, wherein the compensation filter includes abaseband digital filter.
 7. The method of claim 1, further comprisingselecting a finite number of time-domain filter taps among the pluralityof time-domain filter taps.
 8. The method of claim 7, wherein the finitenumber of time-domain filter taps includes one or more positive filtertaps.
 9. The method of claim 8, further comprising adding an extra timedelay in a feedforward path of the compensation filter to include anegative filter tap.
 10. The method of claim 1, wherein the time delayis estimated based on a plurality of minimal least square errors (LSEs)for the corresponding time-domain filter taps.
 11. An apparatuscomprising: a signal generator for generating and sending a single tonesignal at an original frequency; a compensator including a time delayand a plurality of time-domain filter taps; and a compensation logic forperforming a static calibration of the compensator, wherein thecompensation logic is configured to: estimate filter coefficientscorresponding to the plurality of time-domain filter taps of acompensation filter before reception of normal signals based on a staticcalibration scheme; set each of the plurality of time-domain filter tapswith a corresponding estimated filter coefficient; set an initial valuefor a time delay tap to zero or based an estimated value obtained usingthe static calibration scheme; and estimate a filter coefficient for thetime delay tap during reception of a normal signal based on an iterativescheme using an adaptive filter.
 12. The apparatus of claim 11, whereinthe IQMM is a frequency-dependent IQMM (FD-IQMM) or afrequency-independent IQMM (FI-IQMM).
 13. The apparatus of claim 11,wherein the compensation filter is a complex-valued filter.
 14. Theapparatus of claim 11, wherein the compensation filter is a real-valuedfilter including a real-valued scaling factor that feeds a delayedversion of an in-phase (I) path into an output of a real-valued filterof a quadrature (Q) path.
 15. The apparatus of claim 11, wherein thecompensation filter is implemented in a receiver of a wirelesscommunication system.
 16. The apparatus of claim 11, wherein thecompensation filter includes a baseband digital filter.
 17. Theapparatus of claim 11, wherein the compensation logic is furtherconfigured to select a finite number of time-domain filter taps amongthe plurality of time-domain filter taps.
 18. The apparatus of claim 17,wherein the finite number of time-domain filter taps includes one ormore positive filter taps.
 19. The apparatus of claim 18, wherein thecompensation logic is further configured to add an extra time delay in afeedforward path of the compensation filter to include a negative filtertap.
 20. The apparatus of claim 11, wherein the time delay is estimatedbased on a plurality of minimal least square errors (LSEs) for thecorresponding time-domain filter taps.